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For functions in certain classes, the problem of determining: whether two functions are equal, known as the zero-equivalence problem (see Richardson's theorem); [5] the zeroes of a function; whether the indefinite integral of a function is also in the class. [6] Of course, some subclasses of these problems are decidable.
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions).
Lambda calculus is Turing complete, that is, it is a universal model of computation that can be used to simulate any Turing machine. [3] Its namesake, the Greek letter lambda (λ), is used in lambda expressions and lambda terms to denote binding a variable in a function.
Automata are often classified by the class of formal languages they can recognize, as in the Chomsky hierarchy, which describes a nesting relationship between major classes of automata. Automata play a major role in the theory of computation , compiler construction , artificial intelligence , parsing and formal verification .
Software applications that perform symbolic calculations are called computer algebra systems, with the term system alluding to the complexity of the main applications that include, at least, a method to represent mathematical data in a computer, a user programming language (usually different from the language used for the implementation), a ...
Despite being marketed as a supplement, several titles have become widely used as primary textbooks for courses [citation needed] (the Discrete Mathematics and Statistics titles are examples). This is particularly true in settings where an important factor in the selection of a text is the price, such as in community colleges.
An example of a deterministic finite automaton that accepts only binary numbers that are multiples of 3. The state S 0 is both the start state and an accept state. For example, the string "1001" leads to the state sequence S 0, S 1, S 2, S 1, S 0, and is hence accepted.
In these applications, an alphabet is usually required to be a finite set, but is not otherwise restricted. When using automata, regular expressions , or formal grammars as part of string-processing algorithms , the alphabet may be assumed to be the character set of the text to be processed by these algorithms, or a subset of allowable ...
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